Surfactant-induced soluto-capillary motion by a droplet on a thin film

We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem models the lung's thin-film lining following aerosol deposition. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances.;Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A non-linear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines, and the results elucidate the behavior of the thin-film/surfactant system.;We find that surface-tension-induced convection creates film disturbances that increases the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex.;Experiments are conducted to evaluate our theoretical predictions of convection induced by a localized surfactant. Oleic acid and glycerol are the surfactant/thin-film system. The Lagrangian motion of dyed fluid particles are measured, and the results show strong correlation with our theoretical predictions.;A second set of experiments demonstrates the qualitative features of the surfactant/thin-film interaction. These experiments show flow reversal when the gravitational driving force is significant. This is consistent with our theoretical predictions. Additionally, a very thin film ruptures when a high concentration of surfactant is placed on its surface. Our analysis predicts film thinning in this situation, which may lead to the observed film rupture.